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Math Help - Equations and Inequalities

  1. #1
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    Equations and Inequalities

    Question:

    In a certain medical test designed to measure carbohydrate tolerance, an adult drinks 7oz. of a 30% glucose solution. When the test is administered to a child, the glucose concentration must be decreased to 20%. How much 30% glucose solution and how much water should be used to prepare 7 ounces of a 20% glucose solution?

    Book gives answer of: 14/3oz 30% glucose, 7/3oz water

    Nearest I can figure is .3 + x = 7(.2), which gives x = 14/3

    I doubt that's how it works, and if someone can expand on this and help me out, it would be nice.

    Thanks.
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  2. #2
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    You must Equate Something. In this case, you can equate Glucose or Water

    G = Volume of 30% Glucose Solution
    W = Volume of Water

    Equate Glucose

    G(0.3) + W(0.0) = 7(0.2)

    Equate Water

    G(0.7) + W(1.0) = 7(0.8)

    With G + W = 7, each leads to the same solution.

    Looking at your solution, you seem to have (Glucose Ratio) + Water = Glucose. That's no good.
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  3. #3
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    0.7(7 - x) + x = 7(0.8) == Amount H20
    0.3x = 7(0.2) == Amount of glucose

    I get the right numbers, but are the equations correct?

    Thanks.
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  4. #4
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    Quote Originally Posted by sstecken View Post
    0.7(7 - x) + x = 7(0.8) == Amount H20
    0.3x = 7(0.2) == Amount of glucose

    I get the right numbers, but are the equations correct?
    As a good general rule, incorrect equations do not lead to correct results unless you made and error in the solving.

    Of course, there are joke books full of students' antics that managed to lead to correct solutions, but that is not particularly helpful.

    There is no need to cut corners.
    There is no need to do things blindly.

    1) You did not WRITE DOWN your definition of 'x'. Why not?
    2) You did not WRITE DOWN the COMPLETE formulation. Why not.

    Take a good close look at my examples. Clean. Comprehensible. Complete. Easy to follow.

    Look now at yours. It's a buch of symbols that you don't even understand. If you did understand them all, why are you asking if they are correct? Clear and complete equations don't require wondering.

    I'm going to make you tell me what is wrong with your equations. If you had WRITTEN DOWN a clear defintion of 'x', you likely would not have made the mistake that you have made.
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